国内 ETF 期权和股指期权定价研究

RESEARCH ON THE PRICING OF ETF OPTIONS AND STOCK INDEX OPTIONS IN CHINA

方思语

11930276

硕士

数学

王新杰

2021-05-18

2021-06-10

南方科技大学

深圳

股指期权和 ETF 期权作为当前世界最活跃的衍生品之一，在资产配置和风险 管理等领域中都有被广泛地应用。期权产品的价值在全世界范围内都得到了广泛 认同，并且其市场需求也十分旺盛。发展股指期权和 ETF 期权产品作为推进我国 多层次的市场建设的重要举措之一，对资本市场保持健康发展具有重大影响，也 对期权的正确定价提出了更高的要求。常见的期权定价模型 BSM 期权定价模型、 二叉树期权定价模型。BSM 期权定价模型假设标的资产的价格变化遵循几何布朗 运动运动，假设所有交易是在连续的发生，标的资产价格随机游走，根据无风险 套利原则，应用伊藤引理推导出欧式期权的价格；二叉树期权定价模型假设标的 资产的变化服从于布朗运动，通过最小变化时间的不断逼近至 0，将离散变化转化 成连续变化，从而利用倒向逆推法推导出欧式期权的价格。 本文将针对国内现有的沪深 300 股指期权、上证 50ETF 期权、（嘉实）沪深 300ETF 期权和（华泰柏瑞）沪深 300ETF 期权四种期权的看涨看跌期权分别进行 期权定价，对比使用 EGARCH 模型结合滚动窗口获得的预测波动率、隐含波动率 以及 BSM 期权定价模型、二叉树期权定价模型的定价结果的优劣，并利用期权定 价结果与期权价格差分生成交易信号，进行隔日套利交易。结果表明利用过去的 数据选择出的期权定价模型生成的择时信号，可以在短时间内维持较高的正确率， 但是长期来看存在模型失效的风险，需要定期重新选择最优期权定价模型。

As one of the most active derivatives in the world, stock index options and ETF options are widely used in the fields of asset allocation and risk management. The value of option products has been widely recognized all over the world, and its market demand is also very strong. The development of stock index options and ETF optionsproducts is one of the important measures to promote my country's multi-level marketconstruction, which has a significant impact on the maintenance of the healthy development of the capital market, and puts forward higher requirements for the correct pricing of options. Common option pricing models include BSM option pricing model and binary tree option pricing model. The BSM option pricing model assumes that the price change of the underlying asset follows a geometric Brownian motion, assuming that all transactions occur continuously, and that the underlying asset price randomlywalks. According to the principle of risk-free arbitrage, the price of European options isderived by applying Ito's lemma; binary tree The option pricing model assumes that thechange of the underlying asset obeys Brownian motion, and transforms discrete changesinto continuous changes by continuously approaching the minimum change time to 0,thereby using the backward inverse method to derive the price of European options.This article will price the call and put options of the existing CSI 300 stock index options, SSE 50 ETF options, (Harvest) CSI 300 ETF options and (Huatai Bai Rui) CSI 300 ETF options in China, and compare the use of the EGARCH model. Combining the predicted volatility, implied volatility, and the pros and cons of the BSM option pricing model and the binary tree option pricing model obtained in the rolling window, and use the option pricing result and the option price difference to generate trading signals, and carry out the next-day arbitrage transaction. The results show that the timing signalgenerated by the option pricing model selected by the past data can maintain a highaccuracy rate in a short period of time, but there is a risk of model failure in the long run,and the optimal option pricing model needs to be reselected regularly.

布朗运动 B-S-M 模型 二叉树定价模型 EGARCH 模型 期权定价

Brownian motion B-S-M model binary tree pricing model EGARCH model option pricing

中文

独立培养

南方科技大学

方思语. 国内 ETF 期权和股指期权定价研究[D]. 深圳. 南方科技大学,2021.